Arrows on a surface following a path
Unless I've misunderstood the question:

You could make cylinder (a ribbon) to shrinkwrap to the surface, and in its Object > Instancing panel, set its method to 'Faces'

Parent an appropriately oriented arrow-object to the ribbon, and Modifiers > Shrink-Wrap the ribbon to the surface by the projection method that best picks up the normals you're looking for.



You could even adjust the edges between the faces by hand, if you want finer control of the distribution of arrows. The ribbon does not have to be rendered, you can switch that off in the Instancing panel.